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Cos 2Pi

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Welcome to cos 2pi, our post aboutthe cosine of 2pi.

For the cosine of 2pi we use the abbreviation cos for the trigonometric function and write it as cos 2pi.

If you have been looking for what is cos 2pi, or if you have been wondering about cos 2pi radians in degrees, then you are right here, too.

In this post you can find the cos 2pi value, along with identities.

Read on to learn all about the cos of 2pi.

Cos 2Pi Radians

If you want to know what is cos 2pi radians in terms of trigonometry, then navigate straight to the explanations in the next paragraph; what’s ahead in this section is the value of cos 2pi:

cos2pi = 1
cos 2pi = 1
cos 2pi radians = 1

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The cos of 2pi radians is 1, the same as cos of 2pi radians in degrees. To change 2pi radians to degrees multiply 2pi by by 180° / $\pi$ = 360°. Cos 2pi = cos 360 degrees.

Our results of cos2pi have been rounded to five decimal places. If you want cosine 2pi with higher accuracy, then use the calculator below; our tool displays ten decimal places.

To calculate cos 2pi radians insert the angle 2pi in decimal notation, but if you want to calculate cos 2pi in degrees, then you have to press the swap unit button first.

Calculate cos [radians]

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The identities of cosine 2pi are as follows:

= sin (pi/2 + 2pi) = sin 5/2 pi
= sin (pi/2 – 2pi) = sin -3/2 pi

= cos (pi + 2pi) = cos 3 pi
= cos (pi – 2pi) = cos -pi

Note that cos2pi is periodic: cos (2pi + n × 2pi) = cos 2pi, n$\hspace{5px} \in \hspace{5px} \mathbb{Z}$.

There are more formulas for the double angle (2 × 2pi), half angle ((2pi/2)) as well as the sum, difference and products of two angles such as 2pi and β.

You can locate all of them in the respective article found in the header menu. To find everything about cos -2pi click the link. And here is all about sin 2pi, including, for instance, a converter.

In terms of the other five trigonometric functions, cos of 2pi =

  • $\pm \sqrt{1-\sin^{2} 2\pi }$
  • $\pm\frac{1}{\sqrt{1 + \tan^{2} 2\pi}}$
  • $\pm\frac{\cot 2\pi}{\sqrt{1 + \cot^{2} 2\pi}}$
  • $\frac{1}{\sec 2\pi}$
  • $\pm\frac{\sqrt{\csc^{2} (2\pi) – 1} }{\csc 2\pi}$

As the cosine function is the reciprocal of the secant function, 1 / sec 2pi = cos2pi.

In the next part we discuss the trigonometric significance of cos2pi, and there you can also learn what the search calculations form in the sidebar is used for.

What is cos 2Pi?

In a circle with the radius r, the horizontal axis x, and the vertical axis y, 2pi is the angle formed by the two sides x and r; r moving counterclockwise is the positive angle.

As detailed in the unit-circle definition on our homepage, assumed r = 1, in the intersection of the point (x,y) and the circle, x = cos 2pi.

Note that you can locate many terms including the cosine2pi value using the search form. On mobile devices you can find it by scrolling down. Enter, for instance, value of cos2pi.

Along the same lines, using the aforementioned form, can you look up terms such as cos 2pi value, cos 2pi, cos2pi value and what is the cos of 2pi radians, just to name a few.

Given the periodic property of cosine of 2pi, to determine the cosine of an angle > 2pi, e.g. 6 pi, calculate cos 6 pi as cos (6 pi mod 2pi) = cosine of 2pi, or look it up with our form.


The frequently asked questions in the context include what is cos 2pi radians and what is the cos of 2pi degrees for example; reading our content they are no-brainers.

But, if there is something else about cosine 2pi you would like to know, fill in the form on the bottom of this post, or send us an email with a subject line such as cosine 2pi radians.

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